The former United States international, 25, was released by Leeds United in January after a loan spell at Stevenage, and in February he came out as gay and said he was leaving the game that had "hid his secret".
But on Tuesday he trained with the Galaxy, whose coach Bruce Arena said it was "open-ended" as to what his future with the club might hold.
The Chicago Fire hold Rogers' Major League Soccer rights, meaning the Galaxy would need to work out a trade in order to sign him.
"He looked a lot sharper than I thought he would today [Tuesday], given the face he's been away from the game for a while" Arena told the Galaxy's website.
Rogers trained a day after NBA player Jason Collins came out as gay, becoming the first active player from a major US sporting league to do so.
"The timing I guess is good," Arena added. "I think our league is a progressive league. Our league is a league comprised of all different races, colours and creeds, and to be accepting of a gay athlete I don't think is anything that's difficult for our league.
"We've had a great mentality of being open and tolerant of all different kinds of people, views, what have you. We've known Robbie a bunch of years and he's a first-class person and we're only too excited to have him here with us."